With the arrival time difference of left- and right hand GWs induced by velocity birefringence, ref. [1]} proposal a new method for constraining velocity birefringence model independently by measuring the difference of arrival times of two GW polarizations. With this method, it is expect to constrain \(|{\cal W}_1 -{\cal G}_1|\)  to be \(\lesssim 10^{-14} \; {\rm km}\) . This constraint is better than (REF ) by 3 order of magnitudes. The velocity birefringence could also slightly widen or split the peak of the GW waveform [2]}. By checking for waveform peak splitting in the first ever detected GW event, GW150914, ref. [3]} placed the first constraint on velocity birefringence, which corresponds to \(|{\cal W}_1 -{\cal G}_1| \lesssim 10^{-11}\; {\rm km}\) . Recently, the constraints from considering the width of the peak at the maximal amplitude of GW events have been improved significantly with an analysis through 50 GW events in GWTC-1 [4]} and GWTC-2 [5]}.
